Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?

It is (x+y) t miles from the school to Bob's home

Explanation:

Assuming the distance from Bob's home to school is d miles and the time taken is t hours

Distance covered when he had flat tire = d/2, time taken = t/2, rate = x miles/hour

Rate = d/t

x = (d/2) / (t/2)

d = xt miles from Bob's home to halfway the school

distance from halfway the school to the school = d/2, time taken = t/2, rate = y miles/hour

rate = d/t

y = (d/2) / (t/2)

d = yt miles

Total distance from school to Bob's home = xt + yt = (x + y) t miles